WINNIPEG, Manitoba (Reuters) - Saputo Inc, one of Canada's largest dairies, supports ending a domestic milk ingredient pricing system that has angered the United States, Chief Executive Lino Saputo Jr. said on Monday, showing a rare crack in solidarity among processors and the country's sheltered dairy farmers.

The Class 7 pricing agreement, struck in 2016 between Canadian dairy processors including Saputo and farmers, allowed processors to pay lower prices for domestic milk ingredients used to make cheese and yogurt, and to export the rest.

"They want their cake and they want to eat it too," Saputo Jr. said in an interview, referring to farmers. "Which doesn't make sense. You can't hold onto your milk supply-managed system and have a class of milk competing with world markets at the same time."

Saputo Jr.'s remarks came after U.S. Agriculture Secretary Sonny Perdue said on Friday he did not see how the countries could go forward in trade talks without an end to Class 7.

Dairy Farmers of Canada (DFC), the sector's main lobby group, said the industry still speaks with one voice.

"Although (Saputo's) comments took us by surprise, perhaps they are the product of confusion around the notion of flexibility suggested by the federal government," said DFC Chief Executive Jacques Lefebvre, referring to Prime Minister Justin Trudeau's comments to a U.S. television network this month about talks on dairy.

Dairy Processors Association of Canada, of which Saputo is a member, said Class 7 was an effort to "modernize" the system, and its support has not changed.

"We view efforts to expand the dairy sector's contributions to the Canadian economy as positive," DPAC Chief Executive Mathieu Frigon said in a statement.

Canada matches dairy production to domestic consumption, yielding less than 10 percent of the market to imports through tariff-free quotas. Above those quotas, imported dairy faces high tariffs.

Class 7 was struck to create a domestic market for Canadian milk ingredients, after cheaper U.S. volumes that were not subject to high tariffs flooded into Canada. Those U.S. shipments dried up after Class 7 took effect, riling farmers and processors in Wisconsin and New York state.

Saputo Jr. said his company felt forced to support Class 7 through its association. He said he is speaking out now because scrapping Class 7 would be "logical," and less damaging than surrendering additional tariff-free volumes to the United States, similar to what Canada did in trade deals with the European Union and Asia-Pacific nations.

"The system is broken," Saputo Jr. said, adding that it would not surprise him to face a farmer backlash. "The problem is everyone is putting their heads in the sand and no one really wants to find solutions until they're forced. We’re in a position today when we can control our own destiny."